Work Done by a Variable Force

The video tutorial explains how to calculate the work done by a force described by the function f(x) = 24/x^3 Newtons, as an object moves from x = 1 to x = 4. It begins by setting up the integral of the force function over the given limits. The tutorial then demonstrates finding the antiderivative of the function and evaluates the integral to determine the work done. The result is expressed in Newton meters, and the tutorial concludes with a brief discussion on the significance of the units used.

What is the expression for the force function given in the problem?

• f(x) = 24/x^2

• f(x) = 24x^3

• f(x) = 24/x^3

• f(x) = 24x^2

How does the force required to move the object change as x increases from 1 to 4?

• The force first increases then decreases.

• The force decreases.

• The force remains constant.

• The force increases.

What is the integral expression used to calculate the work done?

• Integral from 1 to 4 of 24x^3 dx

• Integral from 1 to 4 of 24/x^3 dx

• Integral from 1 to 4 of 24/x^2 dx

• Integral from 1 to 4 of 24x^2 dx

What is the antiderivative of 24/x^3?

• 24x^2

• -12/x^2

• 12/x^2

• -24/x^2

What is the work done when x is evaluated from 1 to 4?

• 13 Newton meters

• 10.5 Newton meters

• 12 Newton meters

• 11.25 Newton meters

What are the units of the work done in this problem?

• Watts

• Newton seconds

• Joules

• Newton meters